math
posted by dan on .
Show that x^2+y^26x+4y+2=0 and x^2+y^2+8x+2y22=0 are orthogonal.

x^2 + y^2 6x + 4y +2 = 0
can be rewritten as the equation of a circle, as follows.
(x3)^2 + (y+2)^2 9 4 +2 = 0
(x3)^2 + (y+2)^2 = 11
The center of the circle is (3,2) and the radius is sqrt(11).
The other equation can be rewritten
(x+4)^2 + (y+1)^2 = 22 17 = 5
Its center is at (4,1) and the radius is sqrt5
It looks to me like the two curves never intersect; I don't see how they can meet the definition of orthogonal.